An analysis of prospective elementary school teachers’ ill-structured mathematical problem posing activities

Objectives The purposes of this study were to analyze degree of structure and complexity of ill-structured mathematical problems made by prospective elementary teachers. Methods In order to do this, 109 prospective elementary teachers participated in ill-structured mathematical problem posing activities, as a result 24 group work papers were collected. The data was analyzed using framework which determines ill-structured problems and problem complexity. Results The results of this study showed that the degree of structure of the problems posed by prospective teachers varied. The prospective teachers posed problems with relatively high ill-structuredness in terms of authenticity, but with low ill-structuredness in terms of complexity and openness. The prospective teachers posed problems that were low of linguistic complexity but high of mathematical complexity. when prospective teachers asked students to solve problems they posed, most of them expected that difficulties would arise during the phase of carrying out the plan. Conclusions The results indicate that prospective elementary teachers need to develop their competence of posing ill-structured mathematical problems, in particular, there is a need to explore the meaning of openness of ill-structured problems. It also suggests that there is also a need to provide prospective teachers opportunities to anticipate and discuss students’ difficulties in ill-structured problem solving.